| Abstract: |
| Predicting viral evolution presents a significant challenge and is a critical public health priority. We develop a novel model that selects for a new strain with the highest invasion fitness, assuming a trade-off between immune evasion and transmissibility. In case the trade-off function is linear, we can describe the evolutionary patterns following the emergence of subsequent strains by a non-linear difference equation. We provide sufficient criteria for when evolution converges, and successive strains exhibit similar transmissibility. We also identify scenarios characterized by a two-periodic pattern in upcoming strains, indicating a situation where a highly transmissible but not immune-evasive strain is replaced by a less transmissible but highly immune-evasive strain, and vice versa, creating a cyclic pattern. Finally, we show that under certain conditions, viral evolution becomes chaotic and thus future transmissibility rates become unpredictable in the long run. |
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